Affordable Access

deepdyve-link
Publisher Website

Eigenvectors of the discrete Laplacian on regular graphs - a statistical approach

Authors
  • Elon, Yehonatan
Type
Preprint
Publication Date
Apr 17, 2008
Submission Date
Apr 17, 2008
Identifiers
DOI: 10.1088/1751-8113/41/43/435203
Source
arXiv
License
Yellow
External links

Abstract

In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical observations, suggesting that the eigenvectors follow a Gaussian distribution. Following this assumption, we reconstruct some properties of the nodal structure which were observed in numerical simulations, but were not explained so far. We also show that some statistical properties of the nodal pattern cannot be described in terms of a percolation model, as opposed to the suggested correspondence for eigenvectors of 2 dimensional manifolds.

Report this publication

Statistics

Seen <100 times